0
votes
2answers
32 views

Prove that this equation have an non finite number of prime solutions

So the question seeks to answer the following, let $x,y\in\Bbb R$. Prove that there is a non finite number of prime solutions to the following equation: $3x-5y=11$. Our professor says that it's easy ...
0
votes
1answer
29 views

The relationship between the mod value of 2 numbers?

I've been trying to study on my own, the relationship between 2 numbers as you move down the number line from a starting point and could use some help. I believe this could be described as modular ...
1
vote
0answers
25 views

Finding the totient functionlike function for an irrational number like (a+b*sqrt(5)) where a and b are whole numbers mod M where M is a whole number.

I need to find if a value $T$ exists for irrational number of the form $(a+b\cdot \sqrt{5})$ such that $(a+b\cdot \sqrt{5})^T = 1 \pmod M$. Also ,is it possible to find out upper bound for T .
0
votes
1answer
116 views

What will be the multiplicative inverse of square root of 5 with respect to a natural number $M$?

Can such a number $N$ be found such that $\sqrt{5}N \equiv 1 \mod M$? If no,what can be the best approximation for $N$?
0
votes
1answer
172 views

How to Solve an equation with mod for a variable?

I have following equation to be solved, but I am having some trouble in making an understanding and doing so. (d * e) % v = 1 e and v are known. How to solve this ...
1
vote
1answer
57 views

difference between angles

i could not understand exactly what is asked in the following question: What is difference in the degree measures of the angles formed by Hour hand and minute Hand of a clock at $12:35$ and ...
3
votes
1answer
147 views

How to find the smallest positive integer $K$ such that $(K -\lfloor\frac{K}{2}\rfloor + 1)(\lfloor\frac{K}{2}\rfloor + 1) \geq N$

I am writing a program and I would need an explicit formula for the following: The smallest positive integer $K$ such that: $$\left(K - \left\lfloor\frac{K}{2}\right\rfloor + ...
2
votes
2answers
223 views

Equation Calculating what Day it is

Consider this word problem: If the first day of the year is a Monday, what is the 260th day? Answer: Monday Why does this equation work to calculate what day of the week it is: 260 = (7w + 1) [w ...
2
votes
0answers
36 views

For which minimal $k$ true is that ${4}^{k}\cdot n\leq \displaystyle\sum^{n}_{i=1}{a}_{i}^{k}\leq {5}^{k}\cdot n$, ${a}_{i}\in {1,2,3,4,5,6}$?

I've got the following inequality, which bounds Minkowski distance. ${4}^{k}\cdot n\leq \displaystyle\sum^{n}_{i=1}{a}_{i}^{k}\leq {5}^{k}\cdot n$ and values of ${a}_{i}\in {1,2,3,4,5,6}$ We know all ...
5
votes
5answers
212 views

Why is $x^2 \pmod{16}$ always $0, \ 1,\ 4,\ 9$?

With a simple piece of code I could deduce that for any non-negative integer $x$ the value of $x^2 \pmod{16}$ is always a number from the set $\{0, 1, 4, 9\}$. However, the math behind it evades me. ...
0
votes
1answer
115 views

How can I solve $(53 \cdot d) \mod 3432 = 1$?

I do not know how to calculate this problem $$(53 \cdot d) \mod 3432 = 1$$ Given this, what is the value of $d$?
2
votes
2answers
117 views

What is the fastest or usual way to calculate $(\frac{x-1}{2})^2$ mod $x$ if $x$ is odd?

Because: A) for odd $x$ and $x \equiv 1\pmod {4}$ the upper formula is the same as $x - (x-1)/4$ B) for odd $x$ and $x \equiv 3\pmod {4}$ the upper formula is the same as $(x + 1)/4$ Example A) ...
1
vote
1answer
142 views

A rule to determine the crossed out digit

Lets take any integer, $z=abc\cdots$, form the sum of its digits, $a+b+c+\cdots$, subtract this from $z$, cross out any one digit from the result, and denote the sum of the remaining digits by $w$. ...
6
votes
4answers
909 views

calculating n choose k mod one million

I am working on a programming problem where I need to calculate 'n choose k'. I am using the relation formula $$ {n\choose k} = {n\choose k-1} \frac{n-k+1}{k} $$ so I don't have to calculate huge ...
0
votes
4answers
306 views

Finding the last two digits of the expansion of $2^{12n}-6^{4n}$

The question is: Find the last two digits of the expansion of $2^{12n}-6^{4n}$ where $n$ is any positive integer. If we put the value of $n=1$ we would get $2800$. For $n = 2$ the result will ...
4
votes
6answers
396 views

Prove that $(n-m) \mid (n^r - m^r)$

In respect to a larger proof I need to prove that $(n-m) \mid (n^r - m^r) $ (where $\mid$ means divides, i.e., $a \mid b$ means that $b$ modulus $a$ = $0$). I have played around with this for a while ...
5
votes
2answers
251 views

How do I find the lowest $n$ for which $a^n \equiv 1 \pmod{b}$?

This is mostly related to doing large modular exponentiation by hand. For example, a problem I was doing was to find the last 3 digits of $7^{9729}$; that is, find $7^{9729}\bmod{1000}$. Using the ...